CBSE 10th Math Sample Paper 2019 | Q17 Choice 2

This 2019 CBSE class 10 Maths 3 mark question is from Trigonometry. Medium difficulty 3 mark question.

Question 17B: Prove that sin θ(1 + tan θ) + cos θ(1 + cot θ) = sec θ + cosec θ

Video Explanation

Explanatory Answer | CBSE Sample Paper Question 17 Choice 2

LHS: sin θ(1 + tan θ) + cos θ(1 + cot θ)
Substitute tan θ = \\frac{\text{sin θ}}{\text{cos θ}}) and cot θ = \\frac{\text{cos θ}}{\text{sin θ}})
= sin θ (1 + \\frac{\text{sin θ}}{\text{cos θ}}) ) + cos θ (1 + \\frac{\text{cos θ}}{\text{sin θ}}) )
= sin θ ( \\frac{\text{cos θ + sin θ}}{\text{cos θ}})) + cos θ (\\frac{\text{sin θ + cos θ}}{\text{sin θ}}) )
= (sin θ + cos θ) (\\frac{\text{sin θ}}{\text{cos θ}}) + \\frac{\text{cos θ}}{\text{sin θ}}))
= (sin θ + cos θ) (\\frac{\text{sin^2 θ + cos^2 θ}}{\text{sin θ cos θ}})) (We know sin² θ + cos² θ = 1)
= \\frac{\text{sin θ + cos θ}}{\text{sin θ cos θ}}) = \\frac{\text{sin θ}}{\text{sin θ cos θ}}) + \\frac{\text{cos θ}}{\text{sin θ cos θ}})
= \\frac{1}{\text{cos θ}}) + \\frac{1}{\text{sin θ}}) = sec θ + cosec θ